Question

if $tu = 3x$, $uv=x + 8$, and $tv = 16$, what is $tu$?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up equation using segment - addition postulate

Since $TV=TU + UV$, and $TV = 16$, $TU=3x$, $UV=x + 8$, we have the equation $3x+(x + 8)=16$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x+x+8=16$, which simplifies to $4x+8 = 16$.

Step3: Isolate the variable term

Subtract 8 from both sides of the equation: $4x+8−8=16−8$, resulting in $4x=8$.

Step4: Solve for x

Divide both sides of the equation by 4: $\frac{4x}{4}=\frac{8}{4}$, so $x = 2$.

Step5: Find the value of TU

Since $TU = 3x$, substitute $x = 2$ into the expression for $TU$. Then $TU=3\times2=6$.

Answer:

6